Neural–Evolutionary Symbolic Regression with Global Constraints: Constraint-Aware Decoding and Reward Shaping

Xiangdong Wu, Wenjun Wu, Ziyu Wei, Bingrun Chen, Zhenbo Song, Rongye Shi
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:137112-137139, 2026.

Abstract

Symbolic regression aims to discover compact, interpretable mathematical expressions from data, but neural generation is challenging because expressions are tree-structured. Existing neural methods often linearize expression trees into token sequences, facilitating autoregressive modeling but obscuring hierarchical relations and complicating structure-dependent constraint enforcement. We propose GCN-SR, a graph-based symbolic regression framework that generates expressions in an explicit tree-aligned form, making structural context available during decoding. To enable batched generation over variable-topology expressions, we introduce Symbolic Perfect Binary Trees (SPBTs), a fixed-topology scaffold that preserves tree hierarchy while supporting graph-based node-attribute prediction. We further introduce Similarity-Weighted Policy Gradient (SWPG) to incorporate genetic programming (GP) refinement without directly imitating GP-refined elites; instead, refined expressions construct similarity-weighted rewards for samples drawn by the current generator. Experiments on standard symbolic regression benchmarks and ablations show that GCN-SR consistently improves exact recovery over strong neural and hybrid baselines under matched evaluation budgets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-wu26bj, title = {Neural–Evolutionary Symbolic Regression with Global Constraints: Constraint-Aware Decoding and Reward Shaping}, author = {Wu, Xiangdong and Wu, Wenjun and Wei, Ziyu and Chen, Bingrun and Song, Zhenbo and Shi, Rongye}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {137112--137139}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/wu26bj/wu26bj.pdf}, url = {https://proceedings.mlr.press/v306/wu26bj.html}, abstract = {Symbolic regression aims to discover compact, interpretable mathematical expressions from data, but neural generation is challenging because expressions are tree-structured. Existing neural methods often linearize expression trees into token sequences, facilitating autoregressive modeling but obscuring hierarchical relations and complicating structure-dependent constraint enforcement. We propose GCN-SR, a graph-based symbolic regression framework that generates expressions in an explicit tree-aligned form, making structural context available during decoding. To enable batched generation over variable-topology expressions, we introduce Symbolic Perfect Binary Trees (SPBTs), a fixed-topology scaffold that preserves tree hierarchy while supporting graph-based node-attribute prediction. We further introduce Similarity-Weighted Policy Gradient (SWPG) to incorporate genetic programming (GP) refinement without directly imitating GP-refined elites; instead, refined expressions construct similarity-weighted rewards for samples drawn by the current generator. Experiments on standard symbolic regression benchmarks and ablations show that GCN-SR consistently improves exact recovery over strong neural and hybrid baselines under matched evaluation budgets.} }
Endnote
%0 Conference Paper %T Neural–Evolutionary Symbolic Regression with Global Constraints: Constraint-Aware Decoding and Reward Shaping %A Xiangdong Wu %A Wenjun Wu %A Ziyu Wei %A Bingrun Chen %A Zhenbo Song %A Rongye Shi %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-wu26bj %I PMLR %P 137112--137139 %U https://proceedings.mlr.press/v306/wu26bj.html %V 306 %X Symbolic regression aims to discover compact, interpretable mathematical expressions from data, but neural generation is challenging because expressions are tree-structured. Existing neural methods often linearize expression trees into token sequences, facilitating autoregressive modeling but obscuring hierarchical relations and complicating structure-dependent constraint enforcement. We propose GCN-SR, a graph-based symbolic regression framework that generates expressions in an explicit tree-aligned form, making structural context available during decoding. To enable batched generation over variable-topology expressions, we introduce Symbolic Perfect Binary Trees (SPBTs), a fixed-topology scaffold that preserves tree hierarchy while supporting graph-based node-attribute prediction. We further introduce Similarity-Weighted Policy Gradient (SWPG) to incorporate genetic programming (GP) refinement without directly imitating GP-refined elites; instead, refined expressions construct similarity-weighted rewards for samples drawn by the current generator. Experiments on standard symbolic regression benchmarks and ablations show that GCN-SR consistently improves exact recovery over strong neural and hybrid baselines under matched evaluation budgets.
APA
Wu, X., Wu, W., Wei, Z., Chen, B., Song, Z. & Shi, R.. (2026). Neural–Evolutionary Symbolic Regression with Global Constraints: Constraint-Aware Decoding and Reward Shaping. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:137112-137139 Available from https://proceedings.mlr.press/v306/wu26bj.html.

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